The coarse classification of countable abelian groups

We prove that two countable locally finite-by-abelian groups G,H endowed with proper left-invariant metrics are coarsely equivalent if and only if their asymptotic dimensions coincide and the groups are either both finitely-generated or both are infinitely generated. On the other hand, we show that each countable group G that coarsely embeds into a countable abelian group is locally nilpotent-by-finite. Moreover, the group G is locally abelian-by-finite if and only if G is undistorted in the sense that G can be written as the union of countably many finitely generated subgroups G_n such that each G_n is undistorted in G_{n+1} (which means that the identity inclusion from G_n to G_{n+1} is a quasi-isometric embedding with respect to word metrics).Comment: 25 pages. Longer version with new results about FCC groups, locally finite-by-abelian groups, locally nilpotent-by-finite groups

Dimension zero at all scales

We consider the notion of dimension in four categories: the category of (unbounded) separable metric spaces and (metrically proper) Lipschitz maps, and the category of (unbounded) separable metric spaces and (metrically proper) uniform maps. A unified treatment is given to the large scale dimension and the small scale dimension. We show that in all categories a space has dimension zero if and only if it is equivalent to an ultrametric space. Also, 0-dimensional spaces are characterized by means of retractions to subspaces. There is a universal zero-dimensional space in all categories. In the Lipschitz Category spaces of dimension zero are characterized by means of extensions of maps to the unit 0-sphere. Any countable group of asymptotic dimension zero is coarsely equivalent to a direct sum of cyclic groups. We construct uncountably many examples of coarsely inequivalent ultrametric spaces.Comment: 17 pages, To appear in Topology and its Application

The translation of multilingual films: Modes, strategies, constraints and manipulation in the Spanish translations of It's a Free World

British films narrating stories of migration and diaspora are usually multilingual, as directors and scriptwriters wish to depict the linguistic diversity characteristic of today’s British society. But what happens when multilingual films are translated into other languages for distribution abroad? Is multilingualism maintained in the target versions of the film? And when multilingualism is omitted or substituted, is filmic manipulation technically or ideologically bounded? This paper develops a model of analysis which opens up a path in the study of the translation of multilingualism in films by establishing a relationship between translation modes, translation strategies and constraints. I then put the model for analysis to the test in a case study of the dubbing and subtitling into Spanish of one British migration and diasporic film, It’s a Free World … by Ken Loach (2007)